Regulatory Network Reconstruction Using Stochastic Logical Networks

  • Bartek Wilczyński
  • Jerzy Tiuryn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4210)


This paper presents a method for regulatory network reconstruction from experimental data. We propose a mathematical model for regulatory interactions, based on the work of Thomas et al. [25] extended with a stochastic element and provide an algorithm for reconstruction of such models from gene expression time series. We examine mathematical properties of the model and the reconstruction algorithm and test it on expression profiles obtained from numerical simulation of known regulatory networks. We compare the reconstructed networks with the ones reconstructed from the same data using Dynamic Bayesian Networks and show that in these cases our method provides the same or better results. The supplemental materials to this article are available from the website


Regulatory Network Bayesian Network Negative Feedback Loop Discrete State Boolean Network 


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  1. 1.
    Baum, L.E., Peterie, T., Souled, G., Weiss, N.: A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann. Math. Statist. 41(1), 164–171 (1970)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Beal, M.J., Falciani, F., Ghahramani, Z., Rangel, C., Wild, D.L.: A Bayesian approach to reconstructing genetic regulatory networks with hidden factors. Bioinformatics 21(3), 349–356 (2005) (Evaluation Studies)CrossRefGoogle Scholar
  3. 3.
    Chen, K.C., Wang, T.Y., Tseng, H.H., Huang, C.Y., Kao, C.Y.: A stochastic differential equation model for quantifying transcriptional regulatory network in Saccharomyces cerevisiae. Bioinformatics 21(12), 2883–2890 (2005)CrossRefGoogle Scholar
  4. 4.
    Chickering, D.M.: Learning Bayesian networks is NP-complete. In: Proceedings of AI and Statistics (1995)Google Scholar
  5. 5.
    Dojer, N., Gambin, A., Wilczynski, B., Tiuryn, J.: Applying dynamic Bayesian networks to perturbed gene expression data. BMC Bioinformatics 7 (2006)Google Scholar
  6. 6.
    Friedman, N., Linial, M., Nachman, I., Pe’er, D.: Using Bayesian networks to analyze expression data. Journal of Computational Biology 7, 601–620 (2000)CrossRefGoogle Scholar
  7. 7.
    Higham, D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Reviam 43(3), 525–546 (2001)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Husmeier, D.: Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks. Bioinformatics 19(17), 2271–2282 (2003)CrossRefGoogle Scholar
  9. 9.
    Kauffman, S.A.: Homeostasis and differentiation in random genetic control networks. Nature (1969)Google Scholar
  10. 10.
    Larrinaga, A., Naldi, A., Sanchez, L., Thieffry, D., Chaouiya, C.: GINsim: A software suite for the qualitative modelling, simulation and analysis of regulatory networks. Biosystems (January 2006)Google Scholar
  11. 11.
    Mehlhorn, K., Naeher, St.: The LEDA Platform of Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)Google Scholar
  12. 12.
    Mendoza, L., Thieffry, D., Alvarez-Buylla, E.R.: Genetic control of flower morphogenesis in Arabidopsis thaliana: a logical analyssis. Journal of Theoretical Biology (1999)Google Scholar
  13. 13.
    Murphy, K., Mian, S.: Modelling gene expression data using dynamic Bayesian networks. University of California, Berkeley (1999)Google Scholar
  14. 14.
    Ott, S., Imoto, S., Miyano, S.: Finding optimal models for gene networks. In: Proc. of Pacific Symposium in Biocomputing (in press, 2004)Google Scholar
  15. 15.
    Rabiner, L.R.: A tutorial on Hidden Markov Models and selected applications in speech recognition. Proceedings of the IEEE 77(2), 257–286 (1989)CrossRefGoogle Scholar
  16. 16.
    Sanchez, L., Thieffry, D.: A logical analysis of the Drosophila gap-gene system. J. Theor. Biol. 211(2), 115–141 (2001)CrossRefGoogle Scholar
  17. 17.
    Sanchez, L., van Helden, J., Thieffry, D.: Establishement of the dorso-ventral pattern during embryonic development of drosophila melanogasater: a logical analysis. J. Theor. Biol. 189(4), 377–389 (1997)CrossRefGoogle Scholar
  18. 18.
    Sanchez, L., Thieffry, D.: Segmenting the fly embryo: a logical analysis of the pair-rule cross-regulatory module. J. Theor. Biol. 224(4), 517–537 (2003)CrossRefGoogle Scholar
  19. 19.
    Shmulevich, I., Dougherty, E.R., Kim, S., Zhang, W.: Probabilistic Boolean Networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18(2), 261–274 (2002)CrossRefGoogle Scholar
  20. 20.
    Snoussi, E.H.: Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach. Dynamics and stability of systems 4(3-4), 189–207 (1989)MATHMathSciNetGoogle Scholar
  21. 21.
    Spellman, P.T., Sherlock, G., Zhang, M.Q., Iyer, V.R., Anders, K., Eisen, M.B., Brown, P.O., Botstein, D., Futcher, B.: Comprehensive identification of cell cycle regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Molecular Biology of the Cell 9(12), 3273–3297 (1998)Google Scholar
  22. 22.
    Thieffry, D., Sanchez, L.: Alternative epigenetic states understood in terms of specific regulatory structures. Ann. N.Y. Acad. Sci. 981, 135–153 (2002)CrossRefGoogle Scholar
  23. 23.
    Thieffry, D., Sanchez, L.: Dynamical modelling of pattern formation during embryonic development. Curr. Opin. Genet. Dev. 13(4), 326–330 (2003)CrossRefGoogle Scholar
  24. 24.
    Thomas, R.: Boolean formalization of genetic control circuits. Journal of Theoretical Biology 42, 563 (1973)CrossRefGoogle Scholar
  25. 25.
    Thomas, R., D’Ari, R.: Biological Feedback. CRC Press, Boca Raton (1990)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bartek Wilczyński
    • 1
    • 2
  • Jerzy Tiuryn
    • 2
  1. 1.Institute of MathematicsPolish Academy of SciencesWarszawaPoland
  2. 2.Institute of InformaticsWarsaw UniversityWarszawaPoland

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